We consider the case \(d=2\)  as in [1]}, with the fixed sets \(\Omega \) 
and \(S\)  being bounded Lipschitz open connected sets such that \(\Sigma \)  is a Lipschitz 1-manifold. For \(d\ge 3\)  results are available for
the isotropic Griffith model with \(L^p\) -fidelity term (of the type (REF )) in [2]} and with Dirichlet conditions for the displacements at the boundary in [3]}. Moreover, the SDRI energy introduced in [1]} was subsequently found in [5]} (in the setting with Dirichlet conditions instead of the mismatch strains, see (REF ) below) for the wetting regime, i.e., the case where free crystals are assumed to always cover the substrate, as a relaxation formula for both thin films and material voids (without external filaments). The existence results in [5]} are achieved by working with displacements in the functional space \(GSBD_{\infty }^p\) , \(p>1\) , that includes displacements attaining a limit value \(\infty \) , given as a compactification point of \(\mathbb {R}^d\) , in a set of finite perimeter (on which their strain \(e(u)\)  is defined to be zero, see [5]}), which appear to go beyond
the classical framework of small displacements of linearized elasticity, and for the thin-film setting under a bounded-graph assumption on film profiles and without considering delamination.
